Hello,
Mechanical Engineering is a core branch, so if you are interested in its subjects, then you can definitely opt this branch. NIT Jamshedpur is known for its legacy of producing mechanical engieers. Its the best branch of NIT Jamshedpur. You will be placed if you will perform with your best efforts. And about the myth that girls should not opt this stream, there is nothing like that. Your performance and skills speaks. Also mechanical has specialisations which do not require physical work like mechatronics. So go with your interests.